F# Generic Math: how to write function with op_GreaterThan

Question

in F#, how does one write a generic-math step function?

An (Oliver) Heaviside step function is function that returns zero if x is negative, otherwise it retuns one.

Answer 1

Use LanguagePrimitives.GenericZero / GenericOne and let type inference do the rest

// attempt 1:
let inline stepFct1 x =
    let zero = LanguagePrimitives.GenericZero 
    if x > zero then x
    else zero

I had a look at the link you sent with the function you want to implement. FSharpPlus (F#+) may help you to write generic math code since it contains a dedicated Generic Numbers module. Or at least you can grab some techniques from there.

UPDATE

Regarding your updated question, which takes the complexity to a higher level, here is a solution using the latest version of the F#+ project:

let inline CDF(x:^T) : ^T = 
    let num x = fromRational (x </ratio/> 1000000000I)
    let (b1,b2,b3)  = (num 319381530I   , num -356563782I  , num 1781477937I)
    let (b4,b5)     = (num -1821255978I , num 1330274429I)
    let (p , c )    = (num  0231641900I , num 0398942280I)
    let (zero, one, two) = 0G, 1G, 2G
    if x > zero then
        let t = one / (one + p * x) 
        (one - c * exp( -x * x / two)* t * (t*(t*(t*(t*b5+b4)+b3)+b2)+b1)) 
    else
        let t = one / (one - p * x) 
        (c * exp( -x * x / two)* t * (t*(t*(t*(t*b5+b4)+b3)+b2)+b1))

Unfortunately at this time I realised some functions were marked as internal in the library and therefore were not exposed, but I re-created them in a working example here so you can test your function, which works nicely with float and float32.

A new version will be released before end of this year, but in the mean time you can branch it, remove the internals and compile it, or just re-create the functions as I did in the linked example.

If you are interested in Generic Maths feel free to contribute with code or use cases.